Spectral and transport properties of the two-dimensional Lieb lattice

Abstract

The specific topology of the line-centered square lattice (known also as the Lieb lattice) induces remarkable spectral properties such as the macroscopically degenerated zero-energy flat band, the Dirac cone in the low-energy spectrum, and the peculiar Hofstadter-type spectrum in a magnetic field. We study here the properties of the finite Lieb lattice with periodic and vanishing boundary conditions. We investigate the behavior of the flat band induced by disorder and external magnetic and electric fields. We show that in the confined Lieb plaquette threaded by a perpendicular magnetic flux there are edge states with nontrivial behavior. The specific class of twisted edge states, which have alternating chirality, are sensitive to disorder and do not support integer quantum Hall effect (IQHE), but contribute to the longitudinal resistance. The symmetry of the transmittance matrix in the energy range where these states are located is revealed. The diamagnetic moments of the bulk and edge states in the Dirac-Landau domain, and also of the flat states in crossed magnetic and electric fields are shown.